According to the Membrane Paradigm [1]}, [2]}, [3]} the membrane stress tensor in 1+1+2 coordinate split comes as follows
[4]}:
\(t_{ab}=\frac{1}{8\pi G} \left(K h_{ab}-K_{ab} \right),\qquad h_{ab}=\gamma _{ab}-u_a u_b ,\) 
